A novel family of beta mixture models for the differential analysis of DNA methylation data: An application to prostate cancer

by Koyel Majumdar, Romina Silva, Antoinette Sabrina Perry, Ronald William Watson, Andrea Rau, Florence Jaffrezic, Thomas Brendan Murphy, Isobel Claire Gormley

Identifying differentially methylated cytosine-guanine dinucleotide (CpG) sites between benign and tumour samples can assist in understanding disease. However, differential analysis of bounded DNA methylation data often requires data transformation, reducing biological interpretability. To address this, a family of beta mixture models (BMMs) is proposed that (i) objectively infers methylation state thresholds and (ii) identifies differentially methylated CpG sites (DMCs) given untransformed, beta-valued methylation data. The BMMs achieve this through model-based clustering of CpG sites and by employing parameter constraints, facilitating application to different study settings. Inference proceeds via an expectation-maximisation algorithm, with an approximate maximization step providing tractability and computational feasibility. Performance of the BMMs is assessed through thorough simulation studies, and the BMMs are used for differential analyses of DNA methylation data from a prostate cancer study. Intuitive and biologically interpretable methylation state thresholds are inferred and DMCs are identified, including those related to genes such as GSTP1, RASSF1 and RARB, known for their role in prostate cancer development. Gene ontology analysis of the DMCs revealed significant enrichment in cancer-related pathways, demonstrating the utility of BMMs to reveal biologically relevant insights. An R package betaclust facilitates widespread use of BMMs.